23. A wheel with 20 metallic spokes each $1 m$ long is rotated with a speed of $120 rpm$ in a plane perpendicular to a magnetic field of $0.4 G$. The induced emf between the axle and rim of the wheel will be. ($1 G = 10^{-4} T$) (2020-Covid)
Solution:
Induced emf across the rotating rod/spoke is $e = \frac{1}{2} B \omega l^2$.
Here, $\omega = \frac{120 \times 2\pi}{60} = 4\pi rad s^{-1}$ and $B = 0.4 \times 10^{-4} T$.
$e = \frac{1}{2} \times (0.4 \times 10^{-4}) \times (4\pi) \times 1^2 = 0.8\pi \times 10^{-4} \approx 2.51 \times 10^{-4} V$.
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